I'm not sure how things have changed or not, but in the past, it was quite limited who could delete accounts. If it is the same way, you would need some patience until the head admin gets a chance to do so, which could take several days. Maybe the other admins have that ability now, or at least have the ability to change account names so they could change your old account to something different, freeing up the name.
Either way, you could probably speed things up by getting in contact with the admins to discuss your application or to "apply" without using the application form. If you send them the information now, they may just open up the previous account or something when they get a chance.